Integrable magnetic geodesic flows on Lie groups

Details Integrable magnetic geodesic flows on Lie groups Integrable magnetic geodesic flows on Lie groups

2011-11-03

arxiv.org/abs/1111.0726v1

Theoretical and Mathematical Physics, 156, no. 2 (2008) 1127-1141

Physics

Mathematical Physics

16 pages

Scientific paper

10.1007/s11232-008-0083-y

Right-invariant geodesic flows on manifolds of Lie groups associated with 2-cocycles of corresponding Lie algebras are discussed. Algebra of integrals of motion for magnetic geodesic flows is considered and necessary and sufficient condition of integrability in quadratures is formulated. Canonic forms for 2-cocycles of all 4-dimensional Lie algebras are given and integrable cases among them are separated.

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